To determine whether the exponential function [tex]\( f(x) = 10 \cdot \left(\frac{1}{18}\right)^x \)[/tex] represents exponential growth or decay, we need to examine the base of the exponential component.
1. The given function is [tex]\( f(x) = 10 \cdot \left(\frac{1}{18}\right)^x \)[/tex].
2. The base of the exponential term is [tex]\(\frac{1}{18}\)[/tex].
3. In the context of exponential functions, if the base of the exponent is greater than 1, the function represents exponential growth. Conversely, if the base is between 0 and 1, the function represents exponential decay.
4. Here, the base [tex]\(\frac{1}{18}\)[/tex] is a fraction between 0 and 1, as [tex]\(\frac{1}{18} < 1\)[/tex].
5. Since the base is less than 1, we can conclude that the function represents exponential decay.
Therefore, the function represents exponential decay because the base equals [tex]\(\frac{1}{18}\)[/tex].
